Solve frac{sqrt{5}sqrt{6}-sqrt{60}}{sqrt{15}}

$$\frac{ \sqrt{ 5 } \sqrt{ 6 } - \sqrt{ 60 } }{ \sqrt{ 15 } }$$

Evaluate

$$\sqrt{2}-2\approx -0.585786438$$

Solution Steps

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{\sqrt{30}-\sqrt{60}}{\sqrt{15}}$$

Factor 60=2^{2}\times 15. Rewrite the square root of the product \sqrt{2^{2}\times 15} as the product of square roots \sqrt{2^{2}}\sqrt{15}. Take the square root of 2^{2}.

$$\frac{\sqrt{30}-2\sqrt{15}}{\sqrt{15}}$$

Rationalize the denominator of \frac{\sqrt{30}-2\sqrt{15}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\left(\sqrt{30}-2\sqrt{15}\right)\sqrt{15}}{\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\left(\sqrt{30}-2\sqrt{15}\right)\sqrt{15}}{15}$$

Use the distributive property to multiply \sqrt{30}-2\sqrt{15} by \sqrt{15}.

$$\frac{\sqrt{30}\sqrt{15}-2\left(\sqrt{15}\right)^{2}}{15}$$

Factor 30=15\times 2. Rewrite the square root of the product \sqrt{15\times 2} as the product of square roots \sqrt{15}\sqrt{2}.

$$\frac{\sqrt{15}\sqrt{2}\sqrt{15}-2\left(\sqrt{15}\right)^{2}}{15}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{15\sqrt{2}-2\left(\sqrt{15}\right)^{2}}{15}$$

The square of \sqrt{15} is 15.

$$\frac{15\sqrt{2}-2\times 15}{15}$$

Multiply -2 and 15 to get -30.

$$\frac{15\sqrt{2}-30}{15}$$

Divide each term of 15\sqrt{2}-30 by 15 to get \sqrt{2}-2.

$$\sqrt{2}-2$$